Algorithm

Conjugate

Engineering

Aerospace engineering

Optimization algorithm

Computer security

Portfolio

Nonlinear conjugate gradient method

Convergence (economics)

Gradient descent

RADIUS

Selection (genetic algorithm)

Economics

Computer science

Mathematical optimization

Computer network

Line search

Descent (aeronautics)

Mathematics

Asynchronous communication

Broyden–Fletcher–Goldfarb–Shanno algorithm

Mathematical analysis

Artificial intelligence

Geometry

Financial economics

Economic growth

Artificial neural network

Conjugate gradient method

Line (geometry)

AIMS Mathematics

<abstract> In this paper, we present a new hybrid conjugate gradient (CG) approach for solving unconstrained optimization problem. The search direction is a hybrid form of the Fletcher-Reeves (FR) and the Dai-Yuan (DY) CG parameters and is close to the direction of the memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton approach. Independent of the line search, the search direction of the new approach satisfies the descent condition and possess the trust region. We establish the global convergence of the approach for general functions under the Wolfe-type and Armijo-type line search. Using the CUTEr library, numerical results show that the propose approach is more efficient than some existing approaches. Furthermore, we give a practical application of the new approach in optimizing risk in portfolio selection. </abstract>

A hybrid FR-DY conjugate gradient algorithm for unconstrained optimization with application in portfolio selection